Can someone please help me with this maths question?

Hello. I got stuck solving this question on Seneca. Can someone give me a detailed explanation?
QUESTION (calculator allowed):
Solve x^2-3^8x10+3^18=0
The two solutions can be written in a form 3^a and 3^b where n is an integer and a<b. Calculate a+b.
EXPLANATION PROVIDED BY SENECA:
STEP 1) This is a quadratic equation of the form ax^2+bx+c
STEP 2) Its solutions are given by x^2=(-b±√b^2-4ac)/2, with a=1, b=3^8x10, c=3^18
STEP 3) Hence the solutions are: (3^8x10+8x3^8)/2=3^10 and (3^8x10+8x3^8)/2=3^8
STEP 4) Hence, a=8, b=10, a+b=18
Can someone explain why (3^8x10+8x3^8)/2=3^10 and (3^8x10+8x3^8)/2=3^8 in detail?
I would be eternally grateful for your replies.

Not sure where those steps etc come from (or the context of the question) but if you want to find a+b where the roots are 3^a and 3^b, how do you relate the roots to the coefficients of the quadratic. There should be little/no computation required to simply spot a+b, so using the quadratic formula is unnecessary - hence the query about the question/solution.
But you should be able to do some basic index arithemetic to get the (unnecessary) values for 3^a and 3^b, so think about how stuff is represented in terms of powers of 3. Maybe start by factoring 3^8 out of the two terms on the numerator.
There are a few sign/variable typos in the question/solution so Id hope youve gone through it yourself?

Thank you so much for the insight! I’ll retry the questions without the quadratic formula.